Thanks for your detailed response, Mark.
The camera is still under warranty so I can (and probably will) send it back to the camera shop that sold it to me. It was an online purchase. There is no Canon dealer in my city unfortunately.
So, I'll try to explain what I mean by the camera freezes:
It's actually very erratic. Sometimes the button does nothing for several presses. Same on the grip. Most often though, in ONE SHOT mode, when I'm looking through the viewfinder and I press the AF-ON button, the AF word appears in the bottom right corner and won't go out. Focusing gets stuck. I have to press the AF-ON button several times to unstick it. Sometimes the only way to cancel AF is to turn the camera off. Sometimes I can take a picture, sometimes not.
When I have AI SERVO selected and press the AF-ON button it also gets stuck and keeps hunting / trying to focus if I move the camera around. Again, sometimes another press of the AF-ON button will cancel it, sometimes it takes several times and sometimes I can / can't take a photo.
This is all before I take a picture, so the memory card is not even in the equation yet.
I've tried with the grip attached and also not attached. I've also tried with the grip attached but turned off. No difference in any scenario.
If I assign AF & Metering to, for example the asterisk button (usually for AE lock), AF works fine, so the problem is always the AF-On button on the camera and grip. Does that make sense?
Thanks.